{"id":"W3104596182","doi":"","title":"Monotone Hurwitz Numbers in Genus Zero","year":2013,"lang":"en","type":"article","venue":"","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":45,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Waterloo","funders":"","keywords":"Mathematics; Monotone polygon; Hurwitz polynomial; Genus; Hurwitz matrix; Pure mathematics; Zero (linguistics); Combinatorics; Generating function; Discrete mathematics; Mathematical analysis","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["insufficient_payload"],"consensus_categories":["insufficient_payload"],"category_scores_codex":[0.0002561321,0.0001172144,0.0001785012,0.00008079255,0.0000323146,0.00001993018,0.0001552467,0.00008497823,0.007010563],"category_scores_gemma":[0.0001565625,0.00009864001,0.00005019861,0.0002275743,0.00004082011,0.0001633169,0.00005531342,0.0001339884,0.002417387],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00002832715,"about_ca_system_score_gemma":0.00001176421,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0003076586,"about_ca_topic_score_gemma":0.00002618253,"domain_scores_codex":[0.9991559,0.00004738656,0.0002368949,0.0001666492,0.0001305741,0.0002626214],"domain_scores_gemma":[0.9993049,0.0002537572,0.00004487999,0.000292463,0.00002764876,0.00007636117],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.0000255272,0.0004646388,0.01620152,0.0001038255,0.00007030225,0.00002870785,0.002039286,0.000005488953,0.001206864,0.9146592,0.0556803,0.009514326],"study_design_scores_gemma":[0.0003946463,0.00001888315,0.003506846,0.00001371561,0.000006770777,0.00001177325,0.0005206706,0.00007091436,0.002962376,0.9909629,0.00135199,0.0001785676],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8516117,0.00002180227,0.002690926,0.0002318173,0.00008705469,0.0002371519,5.215583e-7,0.00009222626,0.1450267],"genre_scores_gemma":[0.9770948,0.000004321165,0.004238728,0.0002817494,0.00003197568,0.00004522402,0.000001254263,0.00001847071,0.01828349],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1267433,"threshold_uncertainty_score":0.9983593,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02374940075970077,"score_gpt":0.2736419983494092,"score_spread":0.2498925975897084,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}